Using the t-distribution to compare a sample mean to a population mean with unknown variance.
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Practice exam-style student's t-test problems
Given a null hypothesis H0:μ=μ0, we can have any of the following alternative hypotheses
The first two alternative hypotheses are called one-tailed since we only care how far the sample mean, xˉ, is from μ0 in one direction. The last hypothesis is two-tailed because we care how far xˉ is from μ0 regardless of direction.
We can perform a t-test for a single sample against a known mean by on a calculator:
Enter the sample data into a list.
Navigate to T-Test on a calculator.
Select "DATA" and enter the name of the list where sample is stored.
Select the tail type depending on what our alternative hypothesis is (μ0 is the population mean):
=μ0 for a change in mean
<μ0 for a decrease in mean
>μ0 for an increase in mean
Hit calculate, and interpret the p-value as usual.
To compare the means of two samples using a T-test, we use a calculator:
Enter each sample in its own list.
Navigate to 2-SampTTest.
Select "Data", then enter the names of the lists containing the samples.
Select the tail type depending on what our alternative hypothesis is:
μ1=μ2 for different means
<μ2 for first list mean smaller than second
>μ2 for first list mean greater than second
Set "Pooled" to true.
The calculator reports the t-value and p-value, which we interpret as usual.